TSTP Solution File: SET918+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET918+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n015.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 20:40:42 EDT 2024

% Result   : Theorem 0.11s 0.28s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   35 (  12 unt;   0 def)
%            Number of atoms       :  169 (  82 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  211 (  77   ~;  78   |;  50   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :  109 (  97   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f5,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(f6,axiom,
    ! [A,B,C] :
      ( C = set_intersection2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,conjecture,
    ! [A,B,C] :
      ~ ( set_intersection2(unordered_pair(A,B),C) = singleton(A)
        & in(B,C)
        & A != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,negated_conjecture,
    ~ ! [A,B,C] :
        ~ ( set_intersection2(unordered_pair(A,B),C) = singleton(A)
          & in(B,C)
          & A != B ),
    inference(negated_conjecture,[status(cth)],[f10]) ).

fof(f15,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f16,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)],[f4]) ).

fof(f17,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)],[f16]) ).

fof(f18,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)],[f17]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( X0 != singleton(X1)
      | ~ in(X2,X0)
      | X2 = X1 ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f23,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)],[f5]) ).

fof(f24,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)],[f23]) ).

fof(f25,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_1(C,B,A),C)
            | ( sk0_1(C,B,A) != A
              & sk0_1(C,B,A) != B ) )
          & ( in(sk0_1(C,B,A),C)
            | sk0_1(C,B,A) = A
            | sk0_1(C,B,A) = B ) ) ) ),
    inference(skolemization,[status(esa)],[f24]) ).

fof(f28,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != unordered_pair(X1,X2)
      | in(X3,X0)
      | X3 != X2 ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f32,plain,
    ! [A,B,C] :
      ( ( C != set_intersection2(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
            & ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
      & ( C = set_intersection2(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(f33,plain,
    ( ! [A,B,C] :
        ( C != set_intersection2(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_intersection2(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)],[f32]) ).

fof(f34,plain,
    ( ! [A,B,C] :
        ( C != set_intersection2(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_intersection2(A,B)
        | ( ( ~ in(sk0_2(C,B,A),C)
            | ~ in(sk0_2(C,B,A),A)
            | ~ in(sk0_2(C,B,A),B) )
          & ( in(sk0_2(C,B,A),C)
            | ( in(sk0_2(C,B,A),A)
              & in(sk0_2(C,B,A),B) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f33]) ).

fof(f37,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | in(X3,X0)
      | ~ in(X3,X1)
      | ~ in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f47,plain,
    ? [A,B,C] :
      ( set_intersection2(unordered_pair(A,B),C) = singleton(A)
      & in(B,C)
      & A != B ),
    inference(pre_NNF_transformation,[status(esa)],[f11]) ).

fof(f48,plain,
    ? [A,B] :
      ( ? [C] :
          ( set_intersection2(unordered_pair(A,B),C) = singleton(A)
          & in(B,C) )
      & A != B ),
    inference(miniscoping,[status(esa)],[f47]) ).

fof(f49,plain,
    ( set_intersection2(unordered_pair(sk0_5,sk0_6),sk0_7) = singleton(sk0_5)
    & in(sk0_6,sk0_7)
    & sk0_5 != sk0_6 ),
    inference(skolemization,[status(esa)],[f48]) ).

fof(f50,plain,
    set_intersection2(unordered_pair(sk0_5,sk0_6),sk0_7) = singleton(sk0_5),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f51,plain,
    in(sk0_6,sk0_7),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f52,plain,
    sk0_5 != sk0_6,
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ~ in(X0,singleton(X1))
      | X0 = X1 ),
    inference(destructive_equality_resolution,[status(esa)],[f19]) ).

fof(f57,plain,
    ! [X0,X1] : in(X0,unordered_pair(X1,X0)),
    inference(destructive_equality_resolution,[status(esa)],[f28]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( in(X0,set_intersection2(X1,X2))
      | ~ in(X0,X1)
      | ~ in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f37]) ).

fof(f73,plain,
    singleton(sk0_5) = set_intersection2(sk0_7,unordered_pair(sk0_5,sk0_6)),
    inference(paramodulation,[status(thm)],[f50,f15]) ).

fof(f90,plain,
    ! [X0] :
      ( in(sk0_6,set_intersection2(X0,sk0_7))
      | ~ in(sk0_6,X0) ),
    inference(resolution,[status(thm)],[f60,f51]) ).

fof(f164,plain,
    ! [X0] : in(sk0_6,set_intersection2(unordered_pair(X0,sk0_6),sk0_7)),
    inference(resolution,[status(thm)],[f90,f57]) ).

fof(f165,plain,
    ! [X0] : in(sk0_6,set_intersection2(sk0_7,unordered_pair(X0,sk0_6))),
    inference(forward_demodulation,[status(thm)],[f15,f164]) ).

fof(f178,plain,
    in(sk0_6,singleton(sk0_5)),
    inference(paramodulation,[status(thm)],[f73,f165]) ).

fof(f185,plain,
    sk0_6 = sk0_5,
    inference(resolution,[status(thm)],[f178,f53]) ).

fof(f186,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f185,f52]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07  % Problem  : SET918+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.08  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26  % Computer : n015.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Mon Apr 29 22:05:17 EDT 2024
% 0.07/0.27  % CPUTime  : 
% 0.11/0.27  % Drodi V3.6.0
% 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
% 0.11/0.29  % Elapsed time: 0.018721 seconds
% 0.11/0.29  % CPU time: 0.031005 seconds
% 0.11/0.29  % Total memory used: 12.974 MB
% 0.11/0.29  % Net memory used: 12.881 MB
%------------------------------------------------------------------------------