TSTP Solution File: SET971+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET971+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 12:35:38 EDT 2023

% Result   : Theorem 0.16s 0.33s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   27 (  20 unt;   0 def)
%            Number of atoms       :   38 (  24 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   20 (   9   ~;   2   |;   6   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   45 (;  41   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f6,axiom,
    ! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,conjecture,
    ! [A,B,C,D] :
      ( ( subset(A,B)
        & subset(C,D) )
     => set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( ( subset(A,B)
          & subset(C,D) )
       => set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
    inference(negated_conjecture,[status(cth)],[f7]) ).

fof(f9,axiom,
    ! [A,B] :
      ( subset(A,B)
     => set_intersection2(A,B) = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f11,plain,
    ! [A] : set_intersection2(A,A) = A,
    inference(miniscoping,[status(esa)],[f2]) ).

fof(f12,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f19,plain,
    ! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f20,plain,
    ? [A,B,C,D] :
      ( subset(A,B)
      & subset(C,D)
      & set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) != cartesian_product2(A,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f21,plain,
    ( subset(sk0_2,sk0_3)
    & subset(sk0_4,sk0_5)
    & set_intersection2(cartesian_product2(sk0_2,sk0_5),cartesian_product2(sk0_3,sk0_4)) != cartesian_product2(sk0_2,sk0_4) ),
    inference(skolemization,[status(esa)],[f20]) ).

fof(f22,plain,
    subset(sk0_2,sk0_3),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f23,plain,
    subset(sk0_4,sk0_5),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f24,plain,
    set_intersection2(cartesian_product2(sk0_2,sk0_5),cartesian_product2(sk0_3,sk0_4)) != cartesian_product2(sk0_2,sk0_4),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f25,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | set_intersection2(A,B) = A ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_intersection2(X0,X1) = X0 ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f27,plain,
    set_intersection2(sk0_4,sk0_5) = sk0_4,
    inference(resolution,[status(thm)],[f26,f23]) ).

fof(f28,plain,
    set_intersection2(sk0_2,sk0_3) = sk0_2,
    inference(resolution,[status(thm)],[f26,f22]) ).

fof(f30,plain,
    ! [X0,X1] : cartesian_product2(sk0_2,set_intersection2(X0,X1)) = set_intersection2(cartesian_product2(sk0_2,X0),cartesian_product2(sk0_3,X1)),
    inference(paramodulation,[status(thm)],[f28,f19]) ).

fof(f36,plain,
    ! [X0,X1,X2] : cartesian_product2(X0,set_intersection2(X1,X2)) = set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X0,X2)),
    inference(paramodulation,[status(thm)],[f12,f19]) ).

fof(f44,plain,
    ! [X0,X1,X2] : cartesian_product2(X0,set_intersection2(X1,X2)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X0,X1)),
    inference(paramodulation,[status(thm)],[f10,f36]) ).

fof(f45,plain,
    ! [X0,X1,X2] : cartesian_product2(X0,set_intersection2(X1,X2)) = cartesian_product2(X0,set_intersection2(X2,X1)),
    inference(forward_demodulation,[status(thm)],[f36,f44]) ).

fof(f220,plain,
    cartesian_product2(sk0_2,set_intersection2(sk0_5,sk0_4)) != cartesian_product2(sk0_2,sk0_4),
    inference(backward_demodulation,[status(thm)],[f30,f24]) ).

fof(f221,plain,
    cartesian_product2(sk0_2,set_intersection2(sk0_4,sk0_5)) != cartesian_product2(sk0_2,sk0_4),
    inference(forward_demodulation,[status(thm)],[f45,f220]) ).

fof(f222,plain,
    cartesian_product2(sk0_2,sk0_4) != cartesian_product2(sk0_2,sk0_4),
    inference(forward_demodulation,[status(thm)],[f27,f221]) ).

fof(f223,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f222]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10  % Problem  : SET971+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n003.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Tue May 30 10:18:38 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.16/0.32  % Drodi V3.5.1
% 0.16/0.33  % Refutation found
% 0.16/0.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.58  % Elapsed time: 0.039441 seconds
% 0.17/0.58  % CPU time: 0.019036 seconds
% 0.17/0.58  % Memory used: 2.459 MB
%------------------------------------------------------------------------------