TSTP Solution File: SET688+4 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET688+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n025.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 20:40:11 EDT 2024

% Result   : Theorem 0.11s 0.35s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   37 (   8 unt;   0 def)
%            Number of atoms       :  108 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  118 (  47   ~;  34   |;  29   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   59 (  51   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( member(X,A)
         => member(X,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [A,B] :
      ( equal_set(A,B)
    <=> ( subset(A,B)
        & subset(B,A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,conjecture,
    ! [A,B,C] :
      ( ( subset(A,B)
        & ~ equal_set(A,B)
        & subset(B,C)
        & ~ equal_set(B,C) )
     => ~ equal_set(A,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( subset(A,B)
          & ~ equal_set(A,B)
          & subset(B,C)
          & ~ equal_set(B,C) )
       => ~ equal_set(A,C) ),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f14,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( ~ member(X,A)
          | member(X,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f15,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
      & ( subset(A,B)
        | ? [X] :
            ( member(X,A)
            & ~ member(X,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f14]) ).

fof(f16,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [X] :
            ( member(X,A)
            & ~ member(X,B) ) ) ),
    inference(miniscoping,[status(esa)],[f15]) ).

fof(f17,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( member(sk0_0(B,A),A)
          & ~ member(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f16]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f21,plain,
    ! [A,B] :
      ( ( ~ equal_set(A,B)
        | ( subset(A,B)
          & subset(B,A) ) )
      & ( equal_set(A,B)
        | ~ subset(A,B)
        | ~ subset(B,A) ) ),
    inference(NNF_transformation,[status(esa)],[f2]) ).

fof(f22,plain,
    ( ! [A,B] :
        ( ~ equal_set(A,B)
        | ( subset(A,B)
          & subset(B,A) ) )
    & ! [A,B] :
        ( equal_set(A,B)
        | ~ subset(A,B)
        | ~ subset(B,A) ) ),
    inference(miniscoping,[status(esa)],[f21]) ).

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

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

fof(f68,plain,
    ? [A,B,C] :
      ( subset(A,B)
      & ~ equal_set(A,B)
      & subset(B,C)
      & ~ equal_set(B,C)
      & equal_set(A,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f69,plain,
    ? [A,C] :
      ( ? [B] :
          ( subset(A,B)
          & ~ equal_set(A,B)
          & subset(B,C)
          & ~ equal_set(B,C) )
      & equal_set(A,C) ),
    inference(miniscoping,[status(esa)],[f68]) ).

fof(f70,plain,
    ( subset(sk0_3,sk0_5)
    & ~ equal_set(sk0_3,sk0_5)
    & subset(sk0_5,sk0_4)
    & ~ equal_set(sk0_5,sk0_4)
    & equal_set(sk0_3,sk0_4) ),
    inference(skolemization,[status(esa)],[f69]) ).

fof(f71,plain,
    subset(sk0_3,sk0_5),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f72,plain,
    ~ equal_set(sk0_3,sk0_5),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f73,plain,
    subset(sk0_5,sk0_4),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f75,plain,
    equal_set(sk0_3,sk0_4),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f80,plain,
    subset(sk0_4,sk0_3),
    inference(resolution,[status(thm)],[f24,f75]) ).

fof(f89,plain,
    ( spl0_2
  <=> subset(sk0_3,sk0_5) ),
    introduced(split_symbol_definition) ).

fof(f91,plain,
    ( ~ subset(sk0_3,sk0_5)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f89]) ).

fof(f92,plain,
    ( spl0_3
  <=> subset(sk0_5,sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f95,plain,
    ( ~ subset(sk0_3,sk0_5)
    | ~ subset(sk0_5,sk0_3) ),
    inference(resolution,[status(thm)],[f25,f72]) ).

fof(f96,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f95,f89,f92]) ).

fof(f97,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f91,f71]) ).

fof(f98,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f97]) ).

fof(f105,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
      | ~ subset(X2,X1)
      | ~ member(sk0_0(X1,X0),X2) ),
    inference(resolution,[status(thm)],[f20,f18]) ).

fof(f136,plain,
    ! [X0] :
      ( subset(X0,sk0_3)
      | ~ member(sk0_0(sk0_3,X0),sk0_4) ),
    inference(resolution,[status(thm)],[f105,f80]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( subset(X0,sk0_3)
      | ~ subset(X1,sk0_4)
      | ~ member(sk0_0(sk0_3,X0),X1) ),
    inference(resolution,[status(thm)],[f136,f18]) ).

fof(f160,plain,
    ! [X0] :
      ( subset(X0,sk0_3)
      | ~ member(sk0_0(sk0_3,X0),sk0_5) ),
    inference(resolution,[status(thm)],[f146,f73]) ).

fof(f163,plain,
    ( subset(sk0_5,sk0_3)
    | subset(sk0_5,sk0_3) ),
    inference(resolution,[status(thm)],[f160,f19]) ).

fof(f164,plain,
    spl0_3,
    inference(split_clause,[status(thm)],[f163,f92]) ).

fof(f166,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f96,f98,f164]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET688+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.34  % Computer : n025.cluster.edu
% 0.11/0.34  % Model    : x86_64 x86_64
% 0.11/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34  % Memory   : 8042.1875MB
% 0.11/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34  % CPULimit : 300
% 0.11/0.34  % WCLimit  : 300
% 0.11/0.34  % DateTime : Mon Apr 29 21:59:11 EDT 2024
% 0.11/0.34  % CPUTime  : 
% 0.11/0.35  % Drodi V3.6.0
% 0.11/0.35  % Refutation found
% 0.11/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.36  % Elapsed time: 0.018661 seconds
% 0.11/0.36  % CPU time: 0.030701 seconds
% 0.11/0.36  % Total memory used: 11.206 MB
% 0.11/0.36  % Net memory used: 11.139 MB
%------------------------------------------------------------------------------