TSTP Solution File: SET928+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET928+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n022.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 12:35:33 EDT 2023

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   42 (   3 unt;   0 def)
%            Number of atoms       :  104 (  22 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  115 (  53   ~;  43   |;  12   &)
%                                         (   6 <=>;   0  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   52 (;  46   !;   6   ?)

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

fof(f6,axiom,
    ! [A,B,C] :
      ~ ( disjoint(unordered_pair(A,B),C)
        & in(A,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B,C] :
      ~ ( ~ in(A,B)
        & ~ in(C,B)
        & ~ disjoint(unordered_pair(A,C),B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,conjecture,
    ! [A,B,C] :
      ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
    <=> ( ~ in(A,C)
        & ~ in(B,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,negated_conjecture,
    ~ ! [A,B,C] :
        ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
      <=> ( ~ in(A,C)
          & ~ in(B,C) ) ),
    inference(negated_conjecture,[status(cth)],[f8]) ).

fof(f10,axiom,
    ! [A,B] :
      ( disjoint(A,B)
    <=> set_difference(A,B) = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f20,plain,
    ! [A,B,C] :
      ( ~ disjoint(unordered_pair(A,B),C)
      | ~ in(A,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

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

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ~ disjoint(unordered_pair(X0,X1),X2)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f23,plain,
    ! [A,B,C] :
      ( in(A,B)
      | in(C,B)
      | disjoint(unordered_pair(A,C),B) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( in(X0,X1)
      | in(X2,X1)
      | disjoint(unordered_pair(X0,X2),X1) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f25,plain,
    ? [A,B,C] :
      ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
    <~> ( ~ in(A,C)
        & ~ in(B,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f26,plain,
    ? [A,B,C] :
      ( ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
        | ( ~ in(A,C)
          & ~ in(B,C) ) )
      & ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
        | in(A,C)
        | in(B,C) ) ),
    inference(NNF_transformation,[status(esa)],[f25]) ).

fof(f27,plain,
    ( ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = unordered_pair(sk0_2,sk0_3)
      | ( ~ in(sk0_2,sk0_4)
        & ~ in(sk0_3,sk0_4) ) )
    & ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != unordered_pair(sk0_2,sk0_3)
      | in(sk0_2,sk0_4)
      | in(sk0_3,sk0_4) ) ),
    inference(skolemization,[status(esa)],[f26]) ).

fof(f28,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = unordered_pair(sk0_2,sk0_3)
    | ~ in(sk0_2,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f29,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = unordered_pair(sk0_2,sk0_3)
    | ~ in(sk0_3,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f30,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != unordered_pair(sk0_2,sk0_3)
    | in(sk0_2,sk0_4)
    | in(sk0_3,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f31,plain,
    ! [A,B] :
      ( ( ~ disjoint(A,B)
        | set_difference(A,B) = A )
      & ( disjoint(A,B)
        | set_difference(A,B) != A ) ),
    inference(NNF_transformation,[status(esa)],[f10]) ).

fof(f32,plain,
    ( ! [A,B] :
        ( ~ disjoint(A,B)
        | set_difference(A,B) = A )
    & ! [A,B] :
        ( disjoint(A,B)
        | set_difference(A,B) != A ) ),
    inference(miniscoping,[status(esa)],[f31]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | set_difference(X0,X1) = X0 ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | set_difference(X0,X1) != X0 ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f35,plain,
    ( spl0_0
  <=> set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = unordered_pair(sk0_2,sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f36,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = unordered_pair(sk0_2,sk0_3)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f35]) ).

fof(f37,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != unordered_pair(sk0_2,sk0_3)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f35]) ).

fof(f38,plain,
    ( spl0_1
  <=> in(sk0_2,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f39,plain,
    ( in(sk0_2,sk0_4)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f38]) ).

fof(f41,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f28,f35,f38]) ).

fof(f42,plain,
    ( spl0_2
  <=> in(sk0_3,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f45,plain,
    ( spl0_0
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f29,f35,f42]) ).

fof(f46,plain,
    ( ~ spl0_0
    | spl0_1
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f30,f35,f38,f42]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( ~ disjoint(unordered_pair(X0,X1),X2)
      | ~ in(X1,X2) ),
    inference(paramodulation,[status(thm)],[f13,f22]) ).

fof(f64,plain,
    ( disjoint(unordered_pair(sk0_2,sk0_3),sk0_4)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f36,f34]) ).

fof(f75,plain,
    ( ~ in(sk0_3,sk0_4)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f64,f47]) ).

fof(f76,plain,
    ( ~ in(sk0_2,sk0_4)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f64,f22]) ).

fof(f77,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f76,f39]) ).

fof(f78,plain,
    ( ~ spl0_1
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f77]) ).

fof(f79,plain,
    ( ~ disjoint(unordered_pair(sk0_2,sk0_3),sk0_4)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f37,f33]) ).

fof(f80,plain,
    ( in(sk0_2,sk0_4)
    | in(sk0_3,sk0_4)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f79,f24]) ).

fof(f81,plain,
    ( spl0_1
    | spl0_2
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f80,f38,f42,f35]) ).

fof(f83,plain,
    ( ~ spl0_2
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f75,f42,f35]) ).

fof(f84,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f41,f45,f46,f78,f81,f83]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET928+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n022.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue May 30 10:16:57 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.5.1
% 0.13/0.37  % Refutation found
% 0.13/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.62  % Elapsed time: 0.044000 seconds
% 0.22/0.62  % CPU time: 0.023339 seconds
% 0.22/0.62  % Memory used: 3.604 MB
%------------------------------------------------------------------------------