TSTP Solution File: SEU127+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU127+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n008.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 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   25 (  10 unt;   0 def)
%            Number of atoms       :   93 (  10 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  107 (  39   ~;  41   |;  22   &)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   77 (  71   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f4,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(f12,conjecture,
    ! [A,B] : subset(set_intersection2(A,B),A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ! [A,B] : subset(set_intersection2(A,B),A),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f20,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f21,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

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_0(B,A),A)
          & ~ in(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f23]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f28,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)],[f4]) ).

fof(f29,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)],[f28]) ).

fof(f30,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_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)],[f29]) ).

fof(f32,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | ~ in(X3,X0)
      | in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f46,plain,
    ? [A,B] : ~ subset(set_intersection2(A,B),A),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f47,plain,
    ~ subset(set_intersection2(sk0_4,sk0_5),sk0_4),
    inference(skolemization,[status(esa)],[f46]) ).

fof(f48,plain,
    ~ subset(set_intersection2(sk0_4,sk0_5),sk0_4),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_intersection2(X1,X2))
      | in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f32]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( subset(set_intersection2(X0,X1),X2)
      | in(sk0_0(X2,set_intersection2(X0,X1)),X1) ),
    inference(resolution,[status(thm)],[f26,f59]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( subset(set_intersection2(X0,X1),X1)
      | subset(set_intersection2(X0,X1),X1) ),
    inference(resolution,[status(thm)],[f79,f27]) ).

fof(f89,plain,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X1),
    inference(duplicate_literals_removal,[status(esa)],[f88]) ).

fof(f109,plain,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    inference(paramodulation,[status(thm)],[f20,f89]) ).

fof(f156,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f48,f109]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU127+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n008.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 19:46:57 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.13/0.35  % Refutation found
% 0.13/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.37  % Elapsed time: 0.021446 seconds
% 0.19/0.37  % CPU time: 0.042307 seconds
% 0.19/0.37  % Total memory used: 13.032 MB
% 0.19/0.37  % Net memory used: 12.975 MB
%------------------------------------------------------------------------------