TSTP Solution File: SEU159+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU159+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n032.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 12:36:03 EDT 2023

% Result   : Theorem 0.11s 0.28s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   58 (   5 unt;   0 def)
%            Number of atoms       :  192 (  56 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  210 (  76   ~;  93   |;  28   &)
%                                         (  11 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   96 (;  86   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [A,B,C] :
      ( C = unordered_pair(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( D = A
            | D = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f8,negated_conjecture,
    ~ ! [A,B,C] :
        ( subset(unordered_pair(A,B),C)
      <=> ( in(A,C)
          & in(B,C) ) ),
    inference(negated_conjecture,[status(cth)],[f7]) ).

fof(f11,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f12,plain,
    ! [A,B,C] :
      ( ( C != unordered_pair(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | D = A
              | D = B )
            & ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
      & ( C = unordered_pair(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ( D != A
                & D != B ) )
            & ( in(D,C)
              | D = A
              | D = B ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f13,plain,
    ( ! [A,B,C] :
        ( C != unordered_pair(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | D = A
              | D = B )
          & ! [D] :
              ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
    & ! [A,B,C] :
        ( C = unordered_pair(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ( D != A
                & D != B ) )
            & ( in(D,C)
              | D = A
              | D = B ) ) ) ),
    inference(miniscoping,[status(esa)],[f12]) ).

fof(f14,plain,
    ( ! [A,B,C] :
        ( C != unordered_pair(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | D = A
              | D = B )
          & ! [D] :
              ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
    & ! [A,B,C] :
        ( C = unordered_pair(A,B)
        | ( ( ~ in(sk0_0(C,B,A),C)
            | ( sk0_0(C,B,A) != A
              & sk0_0(C,B,A) != B ) )
          & ( in(sk0_0(C,B,A),C)
            | sk0_0(C,B,A) = A
            | sk0_0(C,B,A) = B ) ) ) ),
    inference(skolemization,[status(esa)],[f13]) ).

fof(f15,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != unordered_pair(X1,X2)
      | ~ in(X3,X0)
      | X3 = X1
      | X3 = X2 ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f16,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != unordered_pair(X1,X2)
      | in(X3,X0)
      | X3 != X1 ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f17,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != unordered_pair(X1,X2)
      | in(X3,X0)
      | X3 != X2 ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f21,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f22,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)],[f21]) ).

fof(f23,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)],[f22]) ).

fof(f24,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_1(B,A),A)
          & ~ in(sk0_1(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ in(X2,X0)
      | in(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_1(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_1(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f30,plain,
    ? [A,B,C] :
      ( subset(unordered_pair(A,B),C)
    <~> ( in(A,C)
        & in(B,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f31,plain,
    ? [A,B,C] :
      ( ( subset(unordered_pair(A,B),C)
        | ( in(A,C)
          & in(B,C) ) )
      & ( ~ subset(unordered_pair(A,B),C)
        | ~ in(A,C)
        | ~ in(B,C) ) ),
    inference(NNF_transformation,[status(esa)],[f30]) ).

fof(f32,plain,
    ( ( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
      | ( in(sk0_2,sk0_4)
        & in(sk0_3,sk0_4) ) )
    & ( ~ subset(unordered_pair(sk0_2,sk0_3),sk0_4)
      | ~ in(sk0_2,sk0_4)
      | ~ in(sk0_3,sk0_4) ) ),
    inference(skolemization,[status(esa)],[f31]) ).

fof(f33,plain,
    ( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
    | in(sk0_2,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f34,plain,
    ( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
    | in(sk0_3,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f35,plain,
    ( ~ subset(unordered_pair(sk0_2,sk0_3),sk0_4)
    | ~ in(sk0_2,sk0_4)
    | ~ in(sk0_3,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f36,plain,
    ( spl0_0
  <=> subset(unordered_pair(sk0_2,sk0_3),sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f37,plain,
    ( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f36]) ).

fof(f38,plain,
    ( ~ subset(unordered_pair(sk0_2,sk0_3),sk0_4)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f36]) ).

fof(f39,plain,
    ( spl0_1
  <=> in(sk0_2,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f41,plain,
    ( ~ in(sk0_2,sk0_4)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f39]) ).

fof(f42,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f33,f36,f39]) ).

fof(f43,plain,
    ( spl0_2
  <=> in(sk0_3,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f46,plain,
    ( spl0_0
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f34,f36,f43]) ).

fof(f47,plain,
    ( ~ spl0_0
    | ~ spl0_1
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f35,f36,f39,f43]) ).

fof(f48,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(destructive_equality_resolution,[status(esa)],[f15]) ).

fof(f49,plain,
    ! [X0,X1] : in(X0,unordered_pair(X0,X1)),
    inference(destructive_equality_resolution,[status(esa)],[f16]) ).

fof(f50,plain,
    ! [X0,X1] : in(X0,unordered_pair(X1,X0)),
    inference(destructive_equality_resolution,[status(esa)],[f17]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( subset(unordered_pair(X0,X1),X2)
      | sk0_1(X2,unordered_pair(X0,X1)) = X0
      | sk0_1(X2,unordered_pair(X0,X1)) = X1 ),
    inference(resolution,[status(thm)],[f26,f48]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( subset(unordered_pair(X0,X1),X2)
      | sk0_1(X2,unordered_pair(X1,X0)) = X1
      | sk0_1(X2,unordered_pair(X1,X0)) = X0 ),
    inference(paramodulation,[status(thm)],[f11,f63]) ).

fof(f365,plain,
    ! [X0] :
      ( ~ in(X0,unordered_pair(sk0_2,sk0_3))
      | in(X0,sk0_4)
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f37,f25]) ).

fof(f368,plain,
    ( in(sk0_3,sk0_4)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f365,f50]) ).

fof(f369,plain,
    ( in(sk0_2,sk0_4)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f365,f49]) ).

fof(f370,plain,
    ( $false
    | spl0_1
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f369,f41]) ).

fof(f371,plain,
    ( spl0_1
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f370]) ).

fof(f378,plain,
    ( spl0_3
  <=> sk0_1(sk0_4,unordered_pair(sk0_3,sk0_2)) = sk0_3 ),
    introduced(split_symbol_definition) ).

fof(f379,plain,
    ( sk0_1(sk0_4,unordered_pair(sk0_3,sk0_2)) = sk0_3
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f378]) ).

fof(f381,plain,
    ( spl0_4
  <=> sk0_1(sk0_4,unordered_pair(sk0_3,sk0_2)) = sk0_2 ),
    introduced(split_symbol_definition) ).

fof(f382,plain,
    ( sk0_1(sk0_4,unordered_pair(sk0_3,sk0_2)) = sk0_2
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f381]) ).

fof(f384,plain,
    ( sk0_1(sk0_4,unordered_pair(sk0_3,sk0_2)) = sk0_3
    | sk0_1(sk0_4,unordered_pair(sk0_3,sk0_2)) = sk0_2
    | spl0_0 ),
    inference(resolution,[status(thm)],[f38,f66]) ).

fof(f385,plain,
    ( spl0_3
    | spl0_4
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f384,f378,f381,f36]) ).

fof(f396,plain,
    ( spl0_2
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f368,f43,f36]) ).

fof(f397,plain,
    ( sk0_1(sk0_4,unordered_pair(sk0_2,sk0_3)) = sk0_3
    | ~ spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f11,f379]) ).

fof(f409,plain,
    ( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
    | ~ in(sk0_3,sk0_4)
    | ~ spl0_3 ),
    inference(paramodulation,[status(thm)],[f397,f27]) ).

fof(f410,plain,
    ( spl0_0
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f409,f36,f43,f378]) ).

fof(f421,plain,
    ( sk0_1(sk0_4,unordered_pair(sk0_2,sk0_3)) = sk0_2
    | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f11,f382]) ).

fof(f435,plain,
    ( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
    | ~ in(sk0_2,sk0_4)
    | ~ spl0_4 ),
    inference(paramodulation,[status(thm)],[f421,f27]) ).

fof(f436,plain,
    ( spl0_0
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f435,f36,f39,f381]) ).

fof(f441,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f42,f46,f47,f371,f385,f396,f410,f436]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SEU159+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.08  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.27  % Computer : n032.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit : 300
% 0.07/0.27  % WCLimit  : 300
% 0.07/0.27  % DateTime : Tue May 30 09:09:30 EDT 2023
% 0.07/0.27  % CPUTime  : 
% 0.11/0.27  % Drodi V3.5.1
% 0.11/0.28  % Refutation found
% 0.11/0.28  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.28  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.50  % Elapsed time: 0.016246 seconds
% 0.11/0.50  % CPU time: 0.070747 seconds
% 0.11/0.50  % Memory used: 15.087 MB
%------------------------------------------------------------------------------